Approximating Weighted Duo-Preservation in Comparative Genomics

Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$ between them so as to maximize the number of duos preserved. A duo is any two consecutive characters in a string and it is preserved in the mapping if its two consecutive characters in $s_1$ are mapped to same two consecutive characters in $s_2$. The MDSM problem is known to be NP-hard and there are approximation algorithms for this problem [3, 5, 13], but all of them consider only the "unweighted" version of the problem in the sense that a duo from $s_1$ is preserved by mapping to any same duo in $s_2$ regardless of their positions in the respective strings. However, it is well-desired in comparative genomics to find mappings that consider preserving duos that are "closer" to each other under some distance measure [19]. In this paper, we introduce a generalized version of the problem, called the Maximum-Weight Duo-preservation String Mapping (MWDSM) problem that captures both duos-preservation and duos-distance measures in the sense that mapping a duo from $s_1$ to each preserved duo in $s_2$ has a weight, indicating the "closeness" of the two duos. The objective of the MWDSM problem is to find a mapping so as to maximize the total weight of preserved duos. In this paper, we give a polynomial-time 6-approximation algorithm for this problem.Comment: Appeared in proceedings of the 23rd International Computing and Combinatorics Conference (COCOON 2017

An Integer Programming Formulation of the Minimum Common String Partition problem

We consider the problem of finding a minimum common partition of two strings (MCSP). The problem has its application in genome comparison. MCSP problem is proved to be NP-hard. In this paper, we develop an Integer Programming (IP) formulation for the problem and implement it. The experimental results are compared with the previous state-of-the-art algorithms and are found to be promising.Comment: arXiv admin note: text overlap with arXiv:1401.453

Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linear programming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper version replaces the one submitted on January 10, 2015, due to detected error in the calculation of the variables involved in the ILP model

Development of hybrid metaheuristics based on instance reduction for combinatorial optimization problems

113 p.La tesis presentada describe el desarrollo de algoritmos metaheurísticos híbridos, basados en reducción de instancias de problema. Éstos son enfocados en la resolución de problemas de optimización combinatorial. La motivación original de la investigación radicó en lograr, a través de la reducción de instancias de problemas, el uso efectivo de modelos de programación lineal entera (ILP) sobre problemas que dado su tamaño no admiten el uso directo con esta técnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resolución de problemas de optimización combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempeño de otras metaheurísticas sin el uso de modelos ILP. Los algoritmos presentados mostraron resultados que compiten o superan el estado del arte sobre los problemas Minimum Common String Partition (MCSP), Minimum Covering Arborescence (MCA) y Weighted Independent Domination (WID)